Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping
Abstract Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For instance, the measurement effort poses a critical bottl...
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Nature Portfolio
2025-01-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-024-54859-x |
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| author | Alexander Gresch Martin Kliesch |
| author_facet | Alexander Gresch Martin Kliesch |
| author_sort | Alexander Gresch |
| collection | DOAJ |
| description | Abstract Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For instance, the measurement effort poses a critical bottleneck for variational quantum algorithms. We aim to find the optimal strategy with single-qubit measurements that yields the highest provable accuracy given a total measurement budget. As a central tool, we establish tail bounds for empirical estimators of the energy. They are helpful for identifying measurement settings that improve the energy estimate the most. This task constitutes an NP-hard problem. However, we are able to circumvent this bottleneck and use the tail bounds to develop a practical, efficient estimation strategy, which we call ShadowGrouping. As the name indicates, it combines shadow estimation methods with grouping strategies for Pauli strings. In numerical experiments, we demonstrate that ShadowGrouping improves upon state-of-the-art methods in estimating the electronic ground-state energies of various small molecules, both in provable and practical accuracy benchmarks. Hence, this work provides a promising way, e.g., to tackle the measurement bottleneck associated with quantum many-body Hamiltonians. |
| format | Article |
| id | doaj-art-1fce696474ce4fd69aa343b5cb2cd4d3 |
| institution | Kabale University |
| issn | 2041-1723 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-1fce696474ce4fd69aa343b5cb2cd4d32025-01-19T12:30:44ZengNature PortfolioNature Communications2041-17232025-01-0116111310.1038/s41467-024-54859-xGuaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGroupingAlexander Gresch0Martin Kliesch1Faculty of Mathematics and Natural Sciences, Heinrich Heine University DüsseldorfInstitute for Quantum Inspired and Quantum Optimization, Hamburg University of TechnologyAbstract Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For instance, the measurement effort poses a critical bottleneck for variational quantum algorithms. We aim to find the optimal strategy with single-qubit measurements that yields the highest provable accuracy given a total measurement budget. As a central tool, we establish tail bounds for empirical estimators of the energy. They are helpful for identifying measurement settings that improve the energy estimate the most. This task constitutes an NP-hard problem. However, we are able to circumvent this bottleneck and use the tail bounds to develop a practical, efficient estimation strategy, which we call ShadowGrouping. As the name indicates, it combines shadow estimation methods with grouping strategies for Pauli strings. In numerical experiments, we demonstrate that ShadowGrouping improves upon state-of-the-art methods in estimating the electronic ground-state energies of various small molecules, both in provable and practical accuracy benchmarks. Hence, this work provides a promising way, e.g., to tackle the measurement bottleneck associated with quantum many-body Hamiltonians.https://doi.org/10.1038/s41467-024-54859-x |
| spellingShingle | Alexander Gresch Martin Kliesch Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping Nature Communications |
| title | Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping |
| title_full | Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping |
| title_fullStr | Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping |
| title_full_unstemmed | Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping |
| title_short | Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping |
| title_sort | guaranteed efficient energy estimation of quantum many body hamiltonians using shadowgrouping |
| url | https://doi.org/10.1038/s41467-024-54859-x |
| work_keys_str_mv | AT alexandergresch guaranteedefficientenergyestimationofquantummanybodyhamiltoniansusingshadowgrouping AT martinkliesch guaranteedefficientenergyestimationofquantummanybodyhamiltoniansusingshadowgrouping |